Let \( \Delta=\left|\begin{array}{ccc}2 a_{1} b_{1} & a_{1} b_{2}+a_{2} b_{1} & a_{1} b_{3}+a_{3...
Let \( \Delta=\left|\begin{array}{ccc}2 a_{1} b_{1} & a_{1} b_{2}+a_{2} b_{1} & a_{1} b_{3}+a_{3} b_{1} \\ a_{1} b_{2}+a_{2} b_{1} & 2 a_{2} b_{2} & a_{2} b_{3}+a_{3} b_{2} \\ a_{1} b_{3}+a_{3} b_{1} & a_{3} b_{2}+a_{2} b_{3} & 2 a_{3} b_{3}\end{array}\right| \)
Expressing \( \Delta \) as the product of two determinant, then the value of \( \Delta \).
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